Section II - Basic Vibration Theory

Vibration Analysis Basic Concepts

What is Vibration ? Vibration is a pulsating motion of a machine or a machine part from its original position of rest and can be represented by the formula :

Vibration Amplitude Response =

Dynamic Force Dynamic Resistance

Force Balance C

K M

1. The Exciting Force ‘F’ such as Unbalance 2. The mass of vibrating system ‘M’ 3. The stiffness of vibrating system ‘K’ 4. The damping characteristics ‘C’

Vibration Characteristics 

Amplitude



Frequency



Phase



Direction

Vibration Characteristics 

Amplitude



Frequency



Phase



Direction

Vibration Displacement

Minimum Displacement

Pk-Pk

M

DISPLACEMENT

Max Displacement

Time

Amplitude Units 

Displacement

Pk-Pk

mils or microns

Vibration Velocity

M

RMS

Velocity

Max Velocity

Minimum Velocity

RMS of a Sinusoidal Wave

1 T = __ f

Where T = period of one cycle of the vibration vi = instantaneous velocity t = the variable time

Amplitude Units 

Displacement

Pk-Pk

mils or microns



Velocity

RMS

in/sec or mm/sec

Vibration Acceleration

M

Pk

Acceleration

Max Acceleration

Minimum Acceleration

Amplitude Units (Metric) 

Displacement

Pk-Pk

microns



Velocity

RMS

mm/sec



Acceleration

Pk

g’s

Amplitude Units (Imperial) 

Displacement

Pk-Pk

mils



Velocity

Pk

in/sec



Acceleration

RMS

g’s

Comparison of Amplitude Units Displacement

Velocity

Acceleration

What do they measure? 

Displacement

How far it moves Mils or Microns



Velocity

How fast it moves in/sec or mm/sec



Acceleration

How quickly velocity changes g or in/sec2 or mm/sec2

How Much is too Much ? 

Manufacturers specified limits  End User limits  Comparison with identical machines Same Load, Mounting, Temp, Pressure  Standards specific to type BS 4999 part 142 Electric Motors  General Standards BS-4675 (ISO-2372), VDI - 2056  Historical Data

Conversion of Parameters METRIC UNITS Where:

D=Peak-To-Peak Displacement (µm Pk-Pk) V=Peak Velocity (mm/sec Pk) A=Peak Acceleration (g’s-Pk) F=Frequency (CPM)

V = DF 19,100

V = 3690 A F

A=

D = 9,100V F

A=

D = 70,470,910 F2

VF 3690

DF2 70,470,910

Conversion of Parameters ENGLISH UNITS Where:

D=Peak-To-Peak Displacement (Mils Pk-Pk) V=Peak Velocity (in/sec Pk) A=Peak Acceleration (g’s-Pk) F=Frequency (CPM)

V = DF 19,100

V = 93640 A F

A=

D = 19,100V F

A=

D = 1,790,000,000 F2

VF 93,640

DF2 1,790,000,000

Amplitude Units



Displacement - microns



Total movement, value is from Peak to Peak



Ignores all high frequencies and looks at the low frequency



Acceleration - G-s



Value from the base line to the peak amplitude



Looks a force generated in our machine (High frequency domain)



Velocity RMS - MM/Sec



RMS - root mean square, appears at 0.707 the value of the amplitude



Gives a good overall picture, of the vibration in our machine

Vibration Characteristics 

Amplitude



Frequency



Phase



Direction

Vibration Frequency Vibration Frequency is simply a measure of the numbers of complete cycles that occur in a specified period of time such as ‘Cycles per Second’ or ‘Cycles per Minute’. Frequency is related to the period of vibration by this simple formula : Frequency = 1 / Period

M

DISPLACEMENT

Vibration Frequency

0.5

Time Period = 1.0 mili sec Frequency = 1 / Time Period Frequency = 1 / 10-3 CPS Frequency = 1000 CPS or Hz Frequency = 1000*60 CPM Frequency = 60 kCPM

1.0

Time, mili sec

Significance of Frequency The forces that cause vibration are usually generated through the rotating motion of the machine parts. These forces change in direction or amplitude according to rotational speed of the machine components, most vibration problems will have frequencies that are directly related to the rotational speeds. Vibration Frequency is an Analysis or Diagnostic Tool

Vibration Frequency & Likely Causes Frequency In Terms of RPM 1 X RPM

Most Likely Cause

Other Possible Causes and Remarks

Unbalance

2 X RPM

Mechanical Looseness

3 X RPM

Misalignment

Less than 1 X RPM

Oil Whirl (Less than ½ RPM)

Synchronous AC Line Frequency 2 X Synchronous Line Frequency Many Times RPM Harmonically Related

Electrical Problems

1. Eccentric Journals 2. Misalignment or bent shaft if High Axial Vibration 3. Bad belts if RPM of belt 4. Resonance 5. Reciprocating Forces 6. Electric Problems 1. Misalignment if high axial vibration 2. Reciprocating Forces 3. Resonance 4. Bad belts if 2 X RPM of belt Usually a combination of misalignment and excessive axial clearances (looseness) 1. Bad Belt Drives 2. Background Vibration 3. Sub-Harmonic Resonance 4. Beat Vibrations Common Electrical Problems include broken rotor bars, unbalanced phases in poly-phase system, unequal airgap Rare as a possible unless resonance is exited

High Frequency Not Harmonically Related

Torque Pulses Bad Gears Aerodynamic Forces Hydraulic Forces Mechanical Looseness Reciprocating Forces Bad Anti Friction Bearings

1. 2. 3. 4. 1. 2. 3. 4.

Gear Teeth times RPM if bad gear Number of fan blades times RPM Number of impeller vanes times RPM May occur 2,3,4 and sometimes higher harmonics if severe looseness Bearing Vibration Cavitation, recirculation and flow turbulance cause random, high frequency vibration Improper lubricationof journal bearing (friction exciting vibration Rubbing

Comparison of Parameters F (CPM) 60 600 6,000 60,000 600,000

D (um) 100.00 10.00 1.00 0.10 0.01

V (mm/s) 0.314 0.314 0.314 0.314 0.314

A (g) 0.0002 0.002 0.020 0.201 2.012

Displacement

Force Indicator

10 um

LOG AMPLITUDE (um, mm/s, g)

.20 g

Velocity .314 mm/s .002 g

Fatigue Indicator .314 mm/s .1 um

Acceleration

Stress Indicator

60

600

6K

120K

LOG FREQUENCY (CPM)

600K

Vibration Characteristics 

Amplitude



Frequency



Phase



Direction

What is Phase ? 

The angular reference … at a given frequency … at one instance in time … of a moving part … to a fixed point



The angular reference … at a given frequency … at one instance in time … of two moving parts … to a fixed point

Vibration Phase Phase

is

simply

a

convenient

means

of

determining the relative motion of two vibrating parts of machines. It is measured in degrees or clocks.

Vibration Phase

Phase Relationship as Used With Machinery Vibration

Phase - Phase Vs Amplitude Units 

What we are going to see now is the significant difference between the phase relationships of the three different amplitude units.



This is governed by the laws of physics –

Using Displacement as the base unit, then readings taken in Velocity will lead Displacement by 90°. Acceleration will lead Velocity by 90°, therefor leading Displacement by 180°. Displacement Waveform Velocity Waveform Acceleration Waveform +90°



+90°

It is important to understand the phase shifts with different amplitude units, especially when comparing new data to previous data if the units are different.

Phase - Acquiring Phase Data 

How does the cross channel collect phase data, if ‘phase’ is the relationship between the peak value and the 1x Ts Pulse?



Cross channel uses the first transducer as a reference point, and the second transducer as the comparison. –

Taking the peak value from both waveforms over the same period of time and calculating the difference in the same way as before

Cross Channel Phase

Phase - Acquiring Phase Data 



As stated earlier phase data can be acquired by two means: –

Single Channel

–

Dual Channel

Single Channel Phase Acquisition - How it Works!

Single Channel Phase 

The Phase Angle is calculated using the formula: Phase Angle =

(Difference in Time) X 360° (Time of 1 Revolution)

Phase - Amplitude Characteristics 

In basic vibration training you were introduced to the three units to measure amplitude: –

Velocity • The most common unit used for trending data

• Defined as the ‘Rate of Movement’

–

Acceleration • Used for high speed machinery were impacting is common - Gears, Trouble Shooting Bearings, Peakvue • Defined as ‘Change in Velocity over a period of time’

–

Displacement • Mainly used when looking at relative motion or slow speed machines

• Defined as ‘Total movement from a reference point ’

Phase - Amplitude Characteristics 

Basic vibration also introduced to the effects each unit has on the spectral data –

Velocity • Gives you a good overall level of vibration of both high frequency and low frequency data

–

Acceleration • Accentuates the high frequencies and ignores the low frequencies. Good for looking at impacts.

–

Displacement • Looks at the low frequency data (relative motion) and ignores the high frequency impacting



As expected, the amplitude units effect the time domain much in the same way they do the frequency domain

Phase - Amplitude Characteristics 

Displacement



The spectral plot displays no high frequency data.



This is also apparent in the waveform by the lack of noise riding on the 40 - Dust Filter Fa n No.2 C/Mill sinusoidal shape M72 92 -F1H Fan Inboa rd Horiz ontal P -P Disp in Microns

120

ROU TE SPECTRU M 18- Apr-02 18:04 :29 OVERALL= 5.46 V- DG P-P = 94.2 7 LOAD = 10 0.0 RPM = 141 8. RPS = 23.6 3

90

60

30

0 0

30

60

90

120

Displacem ent in Microns

Frequency in kCPM 80 60

ROU TE WA VEFOR M 18- Apr-02 18:04 :29 P-P = 87.3 8 PK (+) = 55 .85 PK (-) = 54 .21 CR ESTF= 1.81

40 20 0 -20 -40 -60 0

1

2

3 Rev olution Numbe r

4

5

Phase - Amplitude Characteristics Velocity



Viewing the same data linearly across the spectra displays high and low frequency data that was not apparent with ‘Displacement’.



The waveform displays an underlying sinusoidal waveform, but is carrying the high frequency data as well - noisier waveform RMS V eloc ity in m m /S ec



40 - Dust Filter Fa n No.2 C/Mill M72 92 -F1H Fan Inboa rd Horiz ontal

7 6

ROU TE SPECTRU M 18- Apr-02 18:04 :29 OVERALL= 5.46 V- DG RMS = 5.4 4 LOAD = 10 0.0 RPM = 141 8. RPS = 23.6 3

5 4 3 2 1 0 0

30

60

90

120

V elocity in m m /S e c

Frequency in kCPM 20 15

ROU TE WA VEFOR M 18- Apr-02 18:04 :29 RMS = 4.8 4 PK (+) = 15 .15 PK (-) = 12 .86 CR ESTF= 3.13

10 5 0 -5 -10 -15 0

1

2

3 Rev olution Numbe r

4

5

Phase - Amplitude Characteristics Acceleration



The spectra displays a lot of high frequency data, raised noise floor level.



Waveform displays very distinct impacting, common to the high frequency 40 - Dust Filter Fa n No.2 C/Mill M72 92 -F1H Fan Inboa rd Horiz ontal data 0.7 RMS Acce leration in G-s



0.6

Amplitude units also effect ‘phase readings

0.5 0.4 0.3

ROU TE SPECTRU M 18- Apr-02 18:04 :29 OVERALL= 5.46 V- DG RMS = 1.5 0 LOAD = 10 0.0 RPM = 141 8. RPS = 23.6 3

0.2 0.1 0 0

30

60

90

120

Frequency in kCPM

Acc eleration in G-s

8 6

ROU TE WA VEFOR M 18- Apr-02 18:04 :29 RMS = 1.5 5 PK (+) = 6.6 4 PK (-) = 5.9 6 CR ESTF= 4.29

4 2 0 -2 -4 -6 -8 0

1

2

3 Rev olution Numbe r

4

5

Limitations 

There are a few disadvantages to using Single Channel Phase analysis: –

You have to have direct line of sight from the tachometer to the shaft (which is not always possible)

–

Reflective tape needs to be on the shaft (This becomes a problem if the machine is running and no tape is fitted?)

–

Direct sunlight or excessive vibration can cause error between the tachometer reading and the analyzer.

Where to take Readings 

Before we take any phase data it is important to understand why we would want to collect phase data, and what can it tell us?



Phase data is a diagnostic tool and is most commonly used to confirm a suspect fault, such as:



–

Imbalance

–

Misalignment

–

Looseness

–

Resonance

Common terminology used when analyzing phase data are: –

In Phase (0°)- Meaning the relationship between the two points are moving uniformly in the same direction.

–

Out of Phase (180°) - Meaning the relationship between the two points are moving in different directions

Where to take Readings 

We need to acquire phase data in a methodical way to enable us to distinguish certain fault types, (which will be discussed in other topics)



When taking phase data, there is a lot of information we need to remember (amplitudes, in or out of phase and phase angle). To make things easier there is a simple method to follow:



Starting with the ‘Driver’ take and end-end Vertical Phase reading. Note down the Phase and Amplitude results



Next take an end-end Horizontal Phase reading. Again note down the phase and amplitude results

Precautions! 



There are a few precautions to consider when collecting and analyzing phase data. These are: –

1) Transducer Direction

–

2) Observation Errors

Transducer Direction! –



The orientation of a transducer is very important and is the most common cause of interpretation error (more common in the axial direction)

Data taken across a coupling shows 180° phase difference. –

Are these ‘in’ or ‘out’ of phase?

180°

Phase - Transducer Polarity 

The selection of different amplitude units is just one source of hardware induced phase shifts.



Another source of induced phase shift is ‘Transducer Polarity’ This is to do with the internal wiring of the transducer. –

Two identical transducers can be wired the opposite way round to each other causing a 180° phase shift between readings. (Only associated with ‘Cross Channel Phase’

AB



Place the two transducers side by side and acquire a phase reading.



The phase angle should be 0° if it is 180° then this should be deducted from all phase readings thereafter

Phase Summary 

It is important to understand phase as it is a useful tool for doing ‘Investigative’ vibration analysis.



Phase data is a useful tool for finding many common machine faults



–

Imbalance

–

Misalignment

–

Looseness / Soft Foot

It also helps the analyst to visualise the actual movement of the machine –

Like a basic ODS.



Be careful of ‘Transducer Polarity’ and ‘Transducer Direction’ as each can effect the phase angle



Allow a 30° tolerance across all phase data

Vibration Characteristics 

Amplitude



Frequency



Phase



Direction

Vibration Direction 

Vibration is measured in three direction – Horizontal – Vertical – Axial

Measurement Points OB

IB

IB

Motor M1H M1V M1A

OB Pump

M2H M2V M2A

P1H P1V P1A

P2H P2V P2A

Vibration Spectrum

Fast Fourier Transform 

The term ‘FFT’ stands for ‘Fast Fourier Transform’



It is named after an 18th century mathematician called Jean Baptiste Joseph Fourier.



He established: –

Any periodic signal could be represented as a series of sines and cosines. Meaning if you take a time waveform and mathematically calculate the vibration frequency along with their amplitudes, we can convert this in to a more familiar frequency format.

Fast Fourier Transform Complex waveform changes to a simple waveform

The waveform is converted to an amplitude/frequency domain

T im e

T im e

y c n e u q e r F

Amplitude

Amplitude Amplitude



This is called a spectrum

Spectrum





Before we learn how to diagnose potential faults within a spectrum, we need to understand the units of measurement.



The vibration data that is converted from the waveform by the FFT process can be seen very clearly



However there are a few considerations we need to take into account first.



The amplitude scale and the amplitude units are important

As well as the frequency scale and units

Energy in Spectrum

Synchronous Energy 

Synchronous energy - related to turning speed.



We can see from the spectrum that the first peak is at 1 Orders (which means it is 1 x turning speed)



All the other peaks are harmonics off, which means they are related to the first peak Examples of synchronous energy: 1) Imbalance 2) Misalignment

3) Gearmesh

Non- Synchronous Energy 

Non-synchronous energy not related to turning speed



We can see from the spectrum that the first peak is at 10.24 Orders. This is not related to turning speed.

• Examples of non-synchronous energy: •

Bearings

Multiples of belt frequency

Other Machine Speeds

Sub-Synchronous Energy 

Sub-synchronous energy Less than turning speed



The spectrum shows the first impacting peak below 1 Order. This is subsynchronous energy



Examples of subsynchronous energy are:



Belt Frequencies



Other Machine Speeds



Cage Frequencies

Lines of Resolution 

Lines of Resolution (LOR) determine how clear the peaks(data) are defined within our spectrum.



The more lines we have over the same F-max (Maximum frequency scale). The more accurate our data will be



Example. –

The diagram below shows data that has been collected using 400 LOR. Notice how the top of the peaks are capped. When the LOR are increased the data becomes more accurate.

Lines of Resolution TA 16

0.5

L2 - TA 16 -M1H Motor Outboard H orizontal A nalyze Spectrum 13-Mar-01 09:13:53 PK = .7078 LOA D = 100.0 R PM = 1496. R PS = 24.94

PK A cce leration in G -s

0.4

0.3

0.2

0.1

0 0

400

800 Frequency in H z

1200

1600



The spectrum shown displays data at 800 L.O.R with an Fmax of 1600 Hz

Lines of Resolution TA 16

0.20 0.5

L2 - TA 16 -M1H Motor Outboard H orizontal A nalyze Spectrum 13-Mar-01 09:14:16 09:13:53 PK = .3852 .7078 LOA D = 100.0 R PM = 1497. 1496. R PS = 24.95 24.94

PK A cce leration in G -s PK A cce leration in G -s

0.16 0.4



The spectrum shown displays data at 800 L.O.R with an Fmax of 1600 Hz



The second spectrum displays the same data but with 3200 L.O.R over the same Fmax

0.12 0.3

0.08 0.2

0.04 0.1

0 0

400

800 Frequency in H z

1200

1600

Lines of Resolution 

There are 8 LOR settings we can choose from on the analyzer. These start at 100 Lines and go up to 6400 Lines.



The average number of LOR is around 800 Lines for a typical motor/pump set up

To change the LOR settings we need to alter our parameter set. This is done in the Database Setup program Remember. If you double your lines of resolution you double your data collection time.

Questions

mils

3 0.001

0.002

0.003

0.004

sec

3

CPM

mils

3 0.001

0.002

0.004

0.003 T=

3

0.002

F=

1/T

F=

1/0.002

F=

500

Hz

F=

500 x 60

CPM

F=

30000

CPM

Mils P-P

6

sec

60000

90000

CPM

In / sec

3 0.002

0.004

0.006

0.008

sec

3

CPM

In/sec

3 0.002

0.004

0.006

0.008

sec

In / sec Pk

3

3

60000

90000

CPM

2 G’s

0.003

0.006

0.009

0.012

sec

2

CPM

2 G’s

0.003

0.006

0.009

0.012

sec

G’s RMS

2

1.414

20000

30000

CPM

Bonus : if RPM = 1000 What type of Energy is this?

mils

11 0.015

0.030

0.045

0.060

sec Bonus : if RPM = 3000, and Fmax = 50 x RPM, Using LOR = 1600, Calculate BW in CPM & Hz?

In/sec

4.2 0.01

0.02

0.03

sec

Bonus : if RPM = 3600 What type of Energy is this?

10

G’s

0.04

0.032

0.064

0.096

0.112

sec

3 mils

0.9 0.001

0.002

0.003

0.004

sec

CPM

3 mils

0.9 0.001

0.002

0.003

0.004

sec

Mils P-P

6

1.8

60000

90000

CPM

In / sec

10 4 0.005

0.010

0.015

0.020

sec

CPM

In / sec

10

In / sec Pk

4 0.005

0.010

0.015

0.020

sec

10

4

12000

18000

24000

CPM

£100 Acceleration can be measured in which unit? A: mm/sec

B: G-s

C: Microns

D: Hz

£200 The unit RMS or mm/sec can equate to which amplitude measurement? A: Acceleration

B: Displacement

C: Velocity

D: Peak to Peak

£300 Displacement measures which value of a waveform? A: Peak to Peak

B: Peak

C: RMS

D: Average

£500 What are the three units of Frequency?

A: Hz CPM RMS

B: Hz CPM Peak

C: Peak Hz RMS

D: Hz CPM Order

£1,000 The Peak value of a waveform relates to which amplitude measurement? A: Velocity

B: Displacement

C: Average

D: Acceleration

£2000 What does Synchronous energy mean?

A: Below 1 Order

B: Related to 1 Order

C: Bearing Defect

D: Above 1 Order

£4,000 What unit is best used to detect bearing defects?

A: Velocity

B: Displacement

C: Average

D: Acceleration

£8,000 If a motor runs at 1500RPM how many orders would 4500 CPM be? A: 1 Order

B: 2 Orders

C: 2.5 Orders

D: 3 Orders

£16,000 Sub Synchronous Data is?

A: Below 1 Order

B: Equal to 1 Order

C: Up to 5 Orders

D: Above 1 Order

£32,000 A Spectrum is defined as: Amplitude versus …? A: Time

B: CPM

C: Frequency

D: Hz

£64,000 The measurement point P2P is taken where on the machine? A: Inboard D/E

B: Inboard ND/E

C: Outboard ND/E

D: Outboard D/E

£125,000 The measurement point F2A means?

A: Fan inboard axial

B: Fan inboard peakvue

C: Fan inboard vertical

D: Fan outboard axial

£250,000 Locating turning speed will distinguish…?

A: The Frequency Units

B: Peak Amplitudes

C: The Amplitude Units

D: Synchronous Energy

£500,000 Bearing Defects are…?

A: Non Synchronous

B: Synchronous

C: Undetectable

D: Only Detectable with Peakvue

£1,000,000 Electrical defects are what type of energy..?

A: Synchronous

B: Sub Synchronous

C: Undetectable

D: Non Synchronous